Problem: Simplify the following expression: $x = \dfrac{6q^2 - 6q - 12}{q + 1} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $6$ , so we can rewrite the expression: $ x =\dfrac{6(q^2 - 1q - 2)}{q + 1} $ Then we factor the remaining polynomial: $q^2 {-1}q {-2} $ ${1} {-2} = {-1}$ ${1} \times {-2} = {-2}$ $ (q + {1}) (q {-2}) $ This gives us a factored expression: $\dfrac{6(q + {1}) (q {-2})}{q + 1}$ We can divide the numerator and denominator by $(q - 1)$ on condition that $q \neq -1$ Therefore $x = 6(q - 2); q \neq -1$